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A034385 Expansion of (1-16*x)^(-1/4), related to quartic factorial numbers. 6
1, 4, 40, 480, 6240, 84864, 1188096, 16972800, 246105600, 3609548800, 53421322240, 796463349760, 11946950246400, 180123249868800, 2727580640870400, 41459225741230080, 632253192553758720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

A. Straub, V. H. Moll, T. Amdeberhan, The p-adic valuation of k-central binomial coefficients, Acta Arith. 140 (1) (2009) 31-41, eq (1.10)

FORMULA

a(n) = (4^n/n!)*A007696(n), n >= 1, a(0) := 1, A007696(n)=(4*n-3)(!^4) := product(4*j-3, j=1..n); G.f.: (1-16*x)^(-1/4).

D-finite with recurrence: n*a(n) +4*(-4*n+3)*a(n-1)=0. - R. J. Mathar, Jan 28 2020

MATHEMATICA

CoefficientList[Series[1/Surd[1-16x, 4], {x, 0, 20}], x] (* Harvey P. Dale, Aug 06 2018 *)

CROSSREFS

Cf. A007696.

Expansion of (1-b^2*x)^(-1/b): A000984 (b=2), A004987 (b=3), this sequence (b=4), A034688 (b=5), A004993 (b=6), A034835 (b=7), A034977 (b=8), A035024 (b=9), A035308 (b=10).

Sequence in context: A304447 A002705 A235372 * A249927 A218302 A296100

Adjacent sequences:  A034382 A034383 A034384 * A034386 A034387 A034388

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified July 4 10:11 EDT 2022. Contains 355075 sequences. (Running on oeis4.)